#62832

order	256
nilpotency class	2
isoclinism	isoclinic class of #62817
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

4325 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 6 generators on 16 points:

(2,5)(6,8)(9,10)(11,12)(13,14)(15,16);(3,7)(6,8)(10,14)(12,15);(1,2)(3,6)(4,5)(7,8)(9,10,13,14)(11,15,16,12);(9,11)(10,15)(12,14)(13,16);(1,3,4,7)(2,6,5,8)(9,12,13,15)(10,11,14,16);(1,2)(3,6)(4,5)(7,8)(9,11)(10,15)(12,14)(13,16)

Polycyclic presentation:

2^8|c^2=g,e^2=h,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#72272691
Fitting subgroup of	#62832⋊C₃, #72235204, #72235294, …
maximal subgroup of	#186327, #186341, #186355, …
maximal normal subgroup of	#186327, #186341, #186355, …
maximal quotient of	#7626230, #7626242, #7626264, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55820);